Estimate of the pressure when its gradient is the divergence of a measure. Applications
Marc Briane, Juan Casado‐Díaz · ESAIM Control Optimisation and Calculus of Variations · 2010
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L1.